Question

Vorticella is a stalked protozoan that consists of a cell body, which we will treat as a sphere of diameter 20 microns, connected by a long slender stalk (200 microns in total length) to a solid surface. When stimulated by touch, the stalk behaves like a spring with an equilibrium length of zero microns and spring constant k=0.0003 N/m. This means that it rapidly contracts from its extended length thereby drawing the cell body close to the surface. A particular Vorticella cell body initially at rest with its stalk completely extended (length=200 microns) is touched. It begins to rapidly contract. If at some point during contraction, the length of the stalk is x, what is the potential energy stored in the stalk spring? Give your answer in terms of k and x. What is the force exerted by the stalk? If the force exerted by the stalk is completely balanced by the viscous drag on the cell body, what is the velocity of the cell body when the stalk has a length x=100 microns? What is the velocity when the stalk is completely contracted (length x=0)? The drag force on a sphere of radius r is F = 6p?rv. Viscosity of the surrounding medium is ? = 0.01 Pascal-seconds. Starting with the cell body initially at rest, the stalk contracts from a length x = 200 microns to x = 0 microns.What is the total change in energy? What is the work done by the viscous drag?